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On Sumsets of Subsets of Squares

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Abstract

Let \(A\subseteq\{1,\dots,N\}\) be a set of size \(\delta N\). We prove a Bogolyubov–Ruzsa type result that \(A^2+A^2+A^2-A^2-A^2-A^2\) contains a large low-dimensional generalized arithmetic progression.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614, Poznań, Poland

    Tomasz Schoen

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  1. Tomasz Schoen
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Correspondence to Tomasz Schoen.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 314, pp. 311–317 https://doi.org/10.4213/tm4197.

Dedicated to the memory of Professor I. M. Vinogradov

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Schoen, T. On Sumsets of Subsets of Squares. Proc. Steklov Inst. Math. 314, 300–306 (2021). https://doi.org/10.1134/S0081543821040155

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  • DOI: https://doi.org/10.1134/S0081543821040155

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